I can't see how 20% is a 'perfectly just world'. It is not a perfectly just - it is a perfectly random world. If it was 20%, it means that person from every family (wrt. parent's incomes) has equal chance to end up rich or poor, meaning that there is nothing that parents could do to help their child. It means nothing but a totalitarian, concentration camp society, because even if education, healthcare etc. are perfec…
E.g. people whose family is more educated than the average would have better chances to end up in the top quintile by income, regardless of how much money they make.